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Australian Optical Society Photonic bandgaps in woodpile structures G. H. SMITH, L. C. BOTTEN1, R. C. MCPHEDRAN2 AND N. A. NICOROVICI1,2. 1 Department of Mathematical Sciences, University of Technology, Sydney, Broadway, NSW 2007, Australia 2 School of Physics, University of Sydney, NSW 2006, Australia Three-dimensional photonic band gap structures are the ultimate goal for photonic crystals as, unlike one and two-dimensional crystals, they provide for total confinement. One such configuration is the woodpile structure, consisting of layers of dielectric rods with a stacking sequence, which repeats itself every four layers. Our method involves the formulation of plane wave scattering matrices for the structure, derived recursively from the scattering matrices of its component layers, using a Rayleigh method, in which the field quantities are written as multipole expansions. For each layer, there is dispersion in only one direction and thus the 2D-diffraction problem is characterised by a family of 1D problems. Each problem is associated with incidence parameters corresponding to the diffracted orders of the orthogonal grating, leading to scattering matrices that are block diagonal or some permutation thereof. The theory is applied to deduce the spectral properties of the woodpile layering, band diagrams for woodpile photonic crystals, transmission spectra and field plots. Two dimensional projection of the band structure of a woodpile crystal, showing a total band gap. The cylindrical rods have a radius of 0.09 and a refractive index of 3.6. The rods within each layer are separated by 0.65. The distance between layers is 0.22. While the theory we have developed applies to a structure based on cylindrical gratings, it is readily extensible to the structures based on lamellar gratings of rectangular cross-section that are being fabricated by, for example, Sandia Laboratories.